Weierstrass approximation does not hold on the entire Real Line
Hint: if $f_n$ converges uniformly, there exists $n$ such that $|f_n - f_m| \le 1$ for all $m \ge n$.
Weierstrass approximation does not hold on the entire Real Line
Hint: if $f_n$ converges uniformly, there exists $n$ such that $|f_n - f_m| \le 1$ for all $m \ge n$.